What is the difference between a CB radio and a 2-way radio?

A CB is a type of 2-way radio uses a specific set of frequencies, modes, power, and license requirements (usually codified in communication law, rather than a license you apply and pay for). A 2-way radio is radio device that can transmit and receive, usually with another similar to it, but the term "2-way" does not specify frequency, power, mode, or license. It is likely you had an FRS or PMR446 (UK version of FRS) radio. a CB would basically work the same, but not communicate with your buddy, because they use different frequencies and modes.

A CB radio transmits in the 27 MHz band. A 2 way radio could use other frequencies, most likely GMRS or Family Radio Service.

Probably not. a CB radio IS a 2 way radio HOWEVER, so is a police radio, a ham radio, a PMR radio and in fact a mobile phone! Any thing that you can talk through and listen through without wires can be called a two way radio. The chances that your friends 2 way radio is the same as a CB is very remote. To be sure you really need to define what sort, make, model, frequency etc. the 2 way radio is. From that it is possible to find if your CB will work with it. To make matters more complicated a US CB radio is different to a UK CB radio.

There is probably little to no difference. A CB radio is a two way radio on a specific range of frequencies, usually all 40 available channels. A 2-Way radio doesn't specify the frequency band, but is very likely using one or more of the available CB band frequencies, but probably not all 40 channels. Transmit and receive frequency or channel number is what you want to look for.